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# Parabola

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More help with parabolas!

The graph of y = ax^2 + bx + c has an axis of symmetry of x = -18.  If b = 18, then find a.

Dec 17, 2023

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The axis of symmetry of a parabola is a vertical line that passes exactly through the middle of the parabola. Since the axis of symmetry is x = -18, the vertex of the parabola must lie on this line.

We know that the vertex of a parabola is the point where the parabola changes direction from opening upwards to opening downwards, or vice versa. So, in this case, the vertex must be at (-18, y_vertex) for some y_vertex value.

Since b = 18, we can use the formula for the x-coordinate of the vertex of a parabola:

x_vertex = -b / 2a

Plugging in b = 18, we get:

x_vertex = -18 / (2a)

We know that x_vertex = -18, so we can solve for a:

-18 = -18 / (2a)

2a = -18 / -18

2a = 1

a = 1/2

Therefore, the equation of the parabola is:

y = (1/2)x^2 + 18x + c

We still need to find the value of c, the y-intercept. We know that the parabola passes through the point (-18, y_vertex). Plugging this point into the equation, we get:

y_vertex = (1/2)(-18)^2 + 18(-18) + c

Solving for c, we get:

y_vertex = 162 - 324 + c

y_vertex - 162 = c

Since we don't have the actual y_vertex value, we cannot determine the exact value of c. However, we know that the equation of the parabola is:

y = (1/2)x^2 + 18x + (y_vertex - 162)

where y_vertex is the y-coordinate of the vertex, which lies on the line x = -18.

Dec 17, 2023